| Your Results | Global Average | |
|---|---|---|
| Questions | 5 | 5 |
| Correct | 0 | 3.13 |
| Score | 0% | 63% |
The formula for volume of a cube in terms of height (h), length (l), and width (w) is which of the following?
lw x wh + lh |
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h x l x w |
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h2 x l2 x w2 |
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2lw x 2wh + 2lh |
A cube is a rectangular solid box with a height (h), length (l), and width (w). The volume is h x l x w and the surface area is 2lw x 2wh + 2lh.
What is 2a - 9a?
| -7a | |
| 18a | |
| -7 | |
| 11 |
To combine like terms, add or subtract the coefficients (the numbers that come before the variables) of terms that have the same variable raised to the same exponent.
2a - 9a = -7a
The endpoints of this line segment are at (-2, 0) and (2, -4). What is the slope-intercept equation for this line?
| y = -1\(\frac{1}{2}\)x - 2 | |
| y = 1\(\frac{1}{2}\)x + 4 | |
| y = -x - 2 | |
| y = -3x - 2 |
The slope-intercept equation for a line is y = mx + b where m is the slope and b is the y-intercept of the line. From the graph, you can see that the y-intercept (the y-value from the point where the line crosses the y-axis) is -2. The slope of this line is the change in y divided by the change in x. The endpoints of this line segment are at (-2, 0) and (2, -4) so the slope becomes:
m = \( \frac{\Delta y}{\Delta x} \) = \( \frac{(-4.0) - (0.0)}{(2) - (-2)} \) = \( \frac{-4}{4} \)Plugging these values into the slope-intercept equation:
y = -x - 2
Factor y2 - 4y - 21
| (y - 7)(y - 3) | |
| (y - 7)(y + 3) | |
| (y + 7)(y - 3) | |
| (y + 7)(y + 3) |
To factor a quadratic expression, apply the FOIL method (First, Outside, Inside, Last) in reverse. First, find the two Last terms that will multiply to produce -21 as well and sum (Inside, Outside) to equal -4. For this problem, those two numbers are -7 and 3. Then, plug these into a set of binomials using the square root of the First variable (y2):
y2 - 4y - 21
y2 + (-7 + 3)y + (-7 x 3)
(y - 7)(y + 3)
Which of the following statements about math operations is incorrect?
you can multiply monomials that have different variables and different exponents |
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all of these statements are correct |
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you can subtract monomials that have the same variable and the same exponent |
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you can add monomials that have the same variable and the same exponent |
You can only add or subtract monomials that have the same variable and the same exponent. For example, 2a + 4a = 6a and 4a2 - a2 = 3a2 but 2a + 4b and 7a - 3b cannot be combined. However, you can multiply and divide monomials with unlike terms. For example, 2a x 6b = 12ab.